370 
PROFESSOR M. J. M. HILL ON THE MOTION OF FLUID, PART 
Therefore 
l(dd d _ 
~p\dt + U dx +V ^P- 
dy 
Therefore 
d , 
—+u 
dt ' 
1 
clX 
dx 
d\Jr 
dx 
cTX 
dy 
dxp 
dy 
d d d 
dt +U Tx +V dy 
dX d\p 
d d\dx dy 
dx ° dy) 
dX dxp 
dy dx 
= 0 as before. 
dx dx 
dx dy 
dtp d^jr 
dx dy 
But since also 
and 
Therefore 
(d d d\ 
(d , d , d\ , 
'gt +U dx +V dy)^° 
dX d\p dX dxp 
dx dy dy dx c ,• r \ , r/\ i\ 
— —d -some function oi A, xp= / (X, xp) 
3. In what immediately follows p will be supposed constant. Using suffixes to 
denote differential coefficients 
U'/y J (X, 'A) 
Now let g(\, xp) be a function of X, xp such that 
6y(X, xfr ) _ 1 
H /( X, xp) 
Therefore 
therefore 
therefore 
’bgpXrp') 
\ bxp r V iKlJ \ bxp 
^)= 1 
X.jP'y \yg x — 1 
Treating this as a partial differential equation for g, the auxiliary system ol 
equations is 
dx dy da 
